They don't count toward ratings, no. The Arbitron (recently bought by Nielsen, the company that has long done TV ratings) ratings that measure radio listenership are based completely on live listening to over-the-air radio.
TSR tried something different, knowing that their over-the-air signal was very weak, they focused a lot on promoting the higher-quality audio of the app. They did decent numbers with their online and app listenership, but it's difficult to sell those numbers for advertisers for a couple of reasons.
First, the ad agencies that buy most radio and TV ads for their clients won't buy off of anything but hard ratings numbers. So that's an entire segment of companies that just aren't buying the station. Second, it's difficult to sell local companies on online numbers, because those numbers could be coming from anywhere in the world. Their online platform wasn't able to measure location for a very long time, and they tried to sell advertisers on total web hits, rather than unique hits. Where that becomes important is on the app. If you're driving around town and hit a bad cell spot, it'll disconnect you, even if its for just a second. With the metrics they were using, when it reconnected, even if it was only off for a second, it gave them another total hit.
Even with good online numbers and decent response when they would have station remotes, they still couldn't charge ad rates that made them money. Talk radio is expensive to operate because of all the people necessary. They had, at a given time, 7-8 on-air employees. The amount of ads you would have to sell just to stay afloat is astronomical. The owner sunk a lot of his own money in to keep it going, then took on investors. Eventually, the investors wanted a return. They weren't getting it with sports talk. They can with music because an automated satellite-fed oldies station is basically free to run. Agree to carry the 4 minutes of national ads that come off the satellite and you can have the programming for free and you get 8 minutes of ads an hour to sell. It's virtually impossible to lose money with that setup.
I owned a business that advertised with them for awhile over a year ago. We quit for reasons too long to get into, but I was always rooting for them to make it, even though I found it difficult to believe that they would. I knew the numbers involved. I sold my business, partly so I could split time between here and another city for a relationship, so I know what Jason is going through to get back to his family in Cookeville. I hope things work out for everyone involved.